Highest Common Factor of 891, 699, 104 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 891, 699, 104 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 891, 699, 104 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 891, 699, 104 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 891, 699, 104 is 1.

HCF(891, 699, 104) = 1

HCF of 891, 699, 104 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 891, 699, 104 is 1.

Highest Common Factor of 891,699,104 using Euclid's algorithm

Highest Common Factor of 891,699,104 is 1

Step 1: Since 891 > 699, we apply the division lemma to 891 and 699, to get

891 = 699 x 1 + 192

Step 2: Since the reminder 699 ≠ 0, we apply division lemma to 192 and 699, to get

699 = 192 x 3 + 123

Step 3: We consider the new divisor 192 and the new remainder 123, and apply the division lemma to get

192 = 123 x 1 + 69

We consider the new divisor 123 and the new remainder 69,and apply the division lemma to get

123 = 69 x 1 + 54

We consider the new divisor 69 and the new remainder 54,and apply the division lemma to get

69 = 54 x 1 + 15

We consider the new divisor 54 and the new remainder 15,and apply the division lemma to get

54 = 15 x 3 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 891 and 699 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(54,15) = HCF(69,54) = HCF(123,69) = HCF(192,123) = HCF(699,192) = HCF(891,699) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 104 > 3, we apply the division lemma to 104 and 3, to get

104 = 3 x 34 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 104 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(104,3) .

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Frequently Asked Questions on HCF of 891, 699, 104 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 891, 699, 104?

Answer: HCF of 891, 699, 104 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 891, 699, 104 using Euclid's Algorithm?

Answer: For arbitrary numbers 891, 699, 104 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.